Find the derivative of (5 x^ 3 +3 x-1 )(x-1) - Vidyadip

Question

Find the derivative of
$\left(5 x^{3}+3 x-1\right)(x-1)$

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Answer

Let f(x) = $\left(5 x^{3}+3 x-1\right)(x-1)$
By product rule of differentiation,we have,
$f^{\prime}(x)=\left(5 x^{3}+3 x-1\right) \frac{d}{d x}(x-1)$ + $(x-1) \frac{d}{d x}\left(5 x^{3}+3 x+1\right)$
= (5x³+ 3x − 1) $\times$ 1 + (x − 1) $\times$ (15x²+ 3)
= (5x³+ 3x − 1) $+$ (x − 1) $\times$ (15x²+ 3)
= 5x³+ 3x − 1 + 15x³ + 3x − 15x² − 3
= 20x³ - 15x² + 6x - 4

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